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Estimation of agent-based models using sequential Monte Carlo methods

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  • Lux, Thomas

Abstract

Estimation of agent-based models is currently an intense area of research. Recent contributions have to a large extent resorted to simulation-based methods mostly using some form of simulated method of moments estimation (SMM). There is, however, an entire branch of statistical methods that should appear promising, but has to our knowledge never been applied so far to estimate agent-based models in economics and finance: Markov chain Monte Carlo methods designed for state space models or models with latent variables. This later class of models seems particularly relevant as agent-based models typically consist of some latent and some observable variables since not all the characteristics of agents would mostly be observable. Indeed, one might often not only be interested in estimating the parameters of a model, but also to infer the time development of some latent variable. However, agent-based models when interpreted as latent variable models would be typically characterized by non-linear dynamics and non-Gaussian fluctuations and, thus, would require a computational approach to statistical inference. Here we resort to Sequential Monte Carlo (SMC) estimation based on a particle filter. This approach is used here to numerically approximate the conditional densities that enter into the likelihood function of the problem. With this approximation we simultaneously obtain parameter estimates and filtered state probabilities for the unobservable variable(s) that drive(s) the dynamics of the observable time series. In our examples, the observable series will be asset returns (or prices) while the unobservable variables will be some measure of agents' aggregate sentiment. We apply SMC to two selected agent-based models of speculative dynamics with somewhat different flavor. The empirical application to a selection of financial data includes an explicit comparison of the goodness-of-fit of both models.

Suggested Citation

  • Lux, Thomas, 2017. "Estimation of agent-based models using sequential Monte Carlo methods," Economics Working Papers 2017-07, Christian-Albrechts-University of Kiel, Department of Economics.
  • Handle: RePEc:zbw:cauewp:201707
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    References listed on IDEAS

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    Cited by:

    1. Lux, Thomas, 2018. "Inference for nonlinear state space models: A comparison of different methods applied to Markov-switching multifractal models," Economics Working Papers 2018-07, Christian-Albrechts-University of Kiel, Department of Economics.
    2. Adam Majewski & Stefano Ciliberti & Jean-Philippe Bouchaud, 2018. "Co-existence of Trend and Value in Financial Markets: Estimating an Extended Chiarella Model," Papers 1807.11751, arXiv.org.

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    More about this item

    Keywords

    agent-based models; estimation; Markov chain Monte Carlo; particle filter;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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